	
\section{Introduction}\label{sec:introduction}

Information hiding has recently become a major digital 
technology~\cite{1411349,Xie09:BASecurity}, especially with the 
increasing importance and widespread distribution of digital media through the Internet.
Spread-spectrum data-hiding techniques have been widely studied in recent years
under the scope of security. These techniques encompass several schemes, such as 
Improved Spread Spectrum~(ISS), Circular Watermarking~(CW), and Natural 
Watermarking~(NW). Some of these schemes have revealed various 
security issues. On the contrary, it has
been proven in~\cite{Cayre2008} that the Natural Watermarking technique is 
stego-secure. This stego-security is one of the security classes defined 
in~\cite{Cayre2008}, where probabilistic models are used to 
categorize the security of data hiding algorithms in the Watermark Only 
Attack~(WOA) framework.

We have explained in our previous research works~\cite{guyeux13:bc}
that any algorithm can be rewritten as an iterative
process, leading to the possibility to study its
topological behavior. As a concrete example, 
we have shown that the security level of some information hiding algorithms 
(of the spread-spectrum kind) can be studied into a 
novel framework based on unpredictability, as it is understood in the mathematical
theory of chaos~\cite{guyeux13:bc}. 
The key idea motivating our research works is that: \emph{if artificial intelligence (AI)
tools seem to have difficulties to deal with chaos, then steganalyzers (software based 
on AI that try to separate original from stego-contents) may
be proven defective against chaotic information hiding schemes}. Our work
has thus constituted in showing theoretically that such chaotic schemes can be constructed. 
We are not looking to struggle with best available information hiding techniques and
we do not focus on effective and operational aspects, as
our questioning are more locating in a conceptual domain. Among other things, we do
not specify how to chose embedding coefficients, but the way to insert the hidden
message in a selection of these ``least significant coefficient'' in an unpredictable
manner. To say this another
way, our intention is not to realize an hidden channel that does not appear as sleazy
to a steganalyzer, but to construct an information hiding scheme whose behavior cannot
be predicted: supposing that the adversary has anything (algorithm, possible embedding 
coefficient, etc.) but the secret key, we want to determine if he can predict which coefficients
will be finally used, and in which order. To do so, a new class of security has been 
introduced in~\cite{bg10b:ip}, namely the topological security. This new class can be used to study 
some categories of attacks that are difficult to investigate in the existing 
security approach. It also enriches the variety of qualitative and quantitative 
tools that evaluate how strong the security is, thus reinforcing the confidence 
that can be added in a given scheme. 

In addition of being stego-secure, we have proven in~\cite{gfb10:ip} that 
Natural Watermarking (NW) technique is topologically secure. Moreover, this technique 
possesses additional properties of unpredictability, namely, strong transitivity,
topological mixing, and a constant of sensitivity equal to $\frac{N}{2}$~\cite{Guyeux2012}.
However NW are not expansive, which is in our opinion problematic in the Constant-Message 
Attack (CMA) and Known Message Attack (KMA) setups, when we
consider that the attacker has all but the embedding key~\cite{Guyeux2012}. 
Since these initial investigations, our research works in that information hiding field have
thus consisted in searching more secure schemes than NW, regarding the 
concerns presented in the first paragraph of this introduction. The objective
of this review paper is to list the results obtained by following such an approach.

This article is organized as follows. Notations and terminologies are firstly recalled in 
the next section. Then the formerly published $\mathcal{CIW}_1$ chaotic iteration based one-bit watermarking 
process is recalled in detail in Section~\ref{sec:ciw1}. Its steganographic version $\mathcal{CIS}_2$ 
is then explained in Section~\ref{sec:secrypt11}, while Section~\ref{di3sec} presents the
$\mathcal{DI}_3$ process, whose aims is to merge the two previous approaches.
This review article of chaotic iterations based information hiding algorithms 
ends by a conclusion section containing intended future works.
